There are ten time slots for these appointments. For the first time slot, there are 15 different students that can fill the slot. Next appointment, there are only 14 possible students since we already saw one. This goes on and on, 15 x 14 x 13... for 10 different time slots.
15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 = 10,897,286,400
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